Final answer:
To solve the equation 3(b-2)/7 = 2(b+3)/8, we must clear the fractions by cross-multiplying or finding the least common multiple of the denominators and then simplifying. By doing so, we find that the solution for b is 9.
Step-by-step explanation:
The student has presented an algebraic equation 3(b-2)/7 = 2(b+3)/8 to solve for the variable b. To find the solution, we'll clear the fractions by finding a common denominator or by cross-multiplying. Here is a step-by-step breakdown:
- Multiply both sides of the equation by the least common multiple of the denominators 7 and 8 to eliminate fractions. In this case, the least common multiple is 56. The equation becomes 3(b-2)×56/7 = 2(b+3)×56/8.
- Simplify both sides: 24(b-2) = 14(b+3).
- Distribute the numbers to the variables: 24b - 48 = 14b + 42.
- Get all the terms with b on one side and the constants on the other: 24b - 14b = 42 + 48.
- Combine like terms: 10b = 90.
- Divide by 10 to solve for b: b = 9.
Therefore, the solution for b is 9.